We can separate 2 sorts of vowels :
"a", "o", "u" are the strong vowels
"e", "i", "y" are the weak vowels
g + a strong vowel (a,o,u) will be pronounced g like in girl
g + a weak vowel (e,i,y) will be pronounced j like in jerry
You have the same rule for the "c" pronounciation
c + a strong vowel (a,o,u) will be pronounced c like in car
c + a weak ...

I think both pronunciations (with liaison and without liaison) are common. Personally I use both.
With the liaison, the meaning is usually “Ce moment n'est pas encore arrivé”, that is “Not yet”. But I guess the usage varies, and the liaison could be omitted.
However when encore is distinctively stressed (Pas Encore !), the liaison is necessarily omitted… ...

There is a difference.
The "-ai" ending is a close-mid front unrounded vowel ([e]) which is similar to the North American way of saying "play" (but please bear in mind that comparing sounds from one language to another isn't very wise). In French, you'll find the same sound represented by an "é" (e acute). For example, both "grimpai" and "grimpé" are listed ...

It makes sense from a Chinese teacher. The pinyin t is stronger than the French t.
But the pinyin d is somewhere between the French t and French d. I often hear the Chinese render the French t too softly.
The difference between French t and d is less in the mouth than in the throat. The d sound makes use of the vocal folds, whilst the t sound does not.
...

In France the pronunciation is exactly the same : [sa]. But the context will always give you a hint about which one is used.
En France, la prononciation est exactement la même : [sa]. C'est le contexte qui permettra de déterminer lequel des deux est utilisé.

As a rule of thumb, you could pronounce (but not obligatorily) the liaison when meaning "not yet" :
Il n'est pas [z] encore arrivé : he has not arrived yet
Je n'ai pas [z] encore fini : I'm not done yet
In these cases, the use of the liaison might sound a bit posher than without, but that quite depends on the tone too.
However, you should not ...

Nevertheless tu, tué and tout have all three different pronunciations.
In International Phonetic Alphabet
tu is /ty/ Sound
tué is /tɥe/ Sound
tout is /tu/ Sound
For the records, sounds are from Wikimédia.

Unless it's spelled Beauxhommès, I would intuitively not pronounce the final -s. However, note that there's no pronounciation rule for last names.
Also, unlike English, if the original name doesn't have a final -s, putting one when referring to the family is not correct. The family of Dominique Dupont is Les Dupont, not Les Duponts, whereas Homer Simpson's ...

French pronunciation is more regular than English, even if the rules are complicated and do have exceptions. So natives and learners need pronunciation information less often than they do with English. Nonetheless most dictionaries do include phonetic transcriptions, so I'm a little puzzled why you feel a lack of those. (What doesn't exist for French is a ...

If it is pronounced [oi] as I think, you just have to use a dieresis ¨ (tréma in French). It already exists in French, for instance my first name is Lo‌ï‌c, pronounced [loik], as opposed to Lo‌i‌c [lwak].

In English you can refer to it with the standard French way of pronouncing it: /pu'tin/
In Québécois French, however, we say /pu'tsɪn/. You might even hear it sound like “p'tine” /ptsɪn/ in rapid speech, but that would sound really sloppy. Although it's probably not as common as the familiar québécois pronunciation of petite – “p'tite” /ptsɪt/

Essentially, by intonation and pauses. For “80, 16”, one would say:
Quatre-vingt. [pause] Seize.
with a rising intonation at the end of “80”, whereas for “96”, one would say:
Quatre-vingt-seize.
in one go, with a rising intonation at the end of “96” (or falling if at the end of a list or sentence).

That's indeed a very special feature. Usually, words are pronounced the same in their singular and plural forms. In rare cases the endings may change, but the writing changes too (like –ail / –aux or –al / –aux, or œil / yeux, ciel / cieux). Œuf is very peculiar, only the pronunciation changes significantly (just like you described). And bœuf happens to ...

Dropping liquids after consonants (e.g. in words that ends with -ble, -dre, -tre, -fle etc.) is an extremely common feature of everyday pronunciation in French (Grevisse 14th ed., §36c). Pronouncing many final schwas would be the primary reason for the recognition of these consonants and is generally considered either an affectation or a dialectal feature.

A general rule: use whatever is the easiest to pronounce.
In the case of “Je vous ai vu”, I hope you will find [ʒə.vu.z‿e.vy] easier than [ʒə.vu.e.vy], because you would hardly be understood if you omit the liasion.
In “Je voudrais acheter un billet” it doesn't matter much. Personally I use a very light liaison (something between a /z/ and an aspirated ...